1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
|
!**********************************************************************
! Copyright 1998,1999,2000,2001,2002,2005,2007,2008,2009,2010 *
! Andreas Stohl, Petra Seibert, A. Frank, Gerhard Wotawa, *
! Caroline Forster, Sabine Eckhardt, John Burkhart, Harald Sodemann *
! *
! This file is part of FLEXPART. *
! *
! FLEXPART is free software: you can redistribute it and/or modify *
! it under the terms of the GNU General Public License as published by*
! the Free Software Foundation, either version 3 of the License, or *
! (at your option) any later version. *
! *
! FLEXPART is distributed in the hope that it will be useful, *
! but WITHOUT ANY WARRANTY; without even the implied warranty of *
! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
! GNU General Public License for more details. *
! *
! You should have received a copy of the GNU General Public License *
! along with FLEXPART. If not, see <http://www.gnu.org/licenses/>. *
!**********************************************************************
subroutine hanna(z)
! i
!*****************************************************************************
! *
! Computation of \sigma_i and \tau_L based on the scheme of Hanna (1982) *
! *
! Author: A. Stohl *
! *
! 4 December 1997 *
! *
!*****************************************************************************
! *
! Variables: *
! dsigwdz [1/s] vertical gradient of sigw *
! ol [m] Obukhov length *
! sigu, sigv, sigw standard deviations of turbulent velocity fluctuations *
! tlu [s] Lagrangian time scale for the along wind component. *
! tlv [s] Lagrangian time scale for the cross wind component. *
! tlw [s] Lagrangian time scale for the vertical wind component. *
! ust, ustar [m/s] friction velocity *
! wst, wstar [m/s] convective velocity scale *
! *
!*****************************************************************************
use par_mod
use com_mod
use hanna_mod
implicit none
real :: corr,z
!**********************
! 1. Neutral conditions
!**********************
if (h/abs(ol).lt.1.) then
ust=max(1.e-4,ust)
corr=z/ust
sigu=1.e-2+2.0*ust*exp(-3.e-4*corr)
sigw=1.3*ust*exp(-2.e-4*corr)
dsigwdz=-2.e-4*sigw
sigw=sigw+1.e-2
sigv=sigw
tlu=0.5*z/sigw/(1.+1.5e-3*corr)
tlv=tlu
tlw=tlu
!***********************
! 2. Unstable conditions
!***********************
else if (ol.lt.0.) then
! Determine sigmas
!*****************
sigu=1.e-2+ust*(12-0.5*h/ol)**0.33333
sigv=sigu
sigw=sqrt(1.2*wst**2*(1.-.9*zeta)*zeta**0.66666+ &
(1.8-1.4*zeta)*ust**2)+1.e-2
dsigwdz=0.5/sigw/h*(-1.4*ust**2+wst**2* &
(0.8*max(zeta,1.e-3)**(-.33333)-1.8*zeta**0.66666))
! Determine average Lagrangian time scale
!****************************************
tlu=0.15*h/sigu
tlv=tlu
if (z.lt.abs(ol)) then
tlw=0.1*z/(sigw*(0.55-0.38*abs(z/ol)))
else if (zeta.lt.0.1) then
tlw=0.59*z/sigw
else
tlw=0.15*h/sigw*(1.-exp(-5*zeta))
endif
!*********************
! 3. Stable conditions
!*********************
else
sigu=1.e-2+2.*ust*(1.-zeta)
sigv=1.e-2+1.3*ust*(1.-zeta)
sigw=sigv
dsigwdz=-1.3*ust/h
tlu=0.15*h/sigu*(sqrt(zeta))
tlv=0.467*tlu
tlw=0.1*h/sigw*zeta**0.8
endif
tlu=max(10.,tlu)
tlv=max(10.,tlv)
tlw=max(30.,tlw)
if (dsigwdz.eq.0.) dsigwdz=1.e-10
end subroutine hanna
|
